• Quarterly growth data shows that each recession contains at least two quarters of negative growth.
• We found the "Tension Index" (constructed as a moving-average of deviations of growth from its long-term mean) is a reliable indicator of recessions.
• Starts of recessions typically coincide with the tension index decreasing rapidly. Also, all recessions were typified by tension index falling to a value below -5, implying that the tension index has to decrease and become sufficiently low for it to signify the possibility of a recession.
• In order to determine the change in tension index, we found it optimal to utilize the difference of its local averages.
• The recession indicator for any quarter (t) was the difference in the two local averages of the tension index. The first was the average over four quarters from (t) looking ahead (t to t+3) and the second was the average over  four quarters from (t) looking back (t-3 to t).
• As the figure indicates, the recession indicator reaches a local low-point around the starts of recessions and reaches a local high-point around the ends of recessions.

Recession-Indicator Based on Changes in the Tension Index

Algorithm to Date the Start and End of a Recession

• A quarter (t) can serve as a potential candidate for the start of a recession if at least two negative growth rates are observed in the four quarter forward-looking window [t, t +3]. For example, let t be the first quarter encountered with at least two negative growth rates in the windows [t, t +3]. Let t+k be the last contiguous quarter to satisfy this criterion. That is, the sequence of dates t, t+1, ..., t+k serve as potential starts for a recession.

• Given the sequence of potential start-dates ([t; t +k]), quarters t +3, t+4, ..., t+k+3 automatically serve as potential candidates for the end of the recession.

• Having identified a contiguous sequence of quarters as potential start-dates, we choose the optimal start-date according to the following criteria.
  
  1. Quarters with the tension index larger than -5 are eliminated.
  
  2. Among the remaining quarters, the one corresponding to the smallest value of the recession-indicator is chosen as the optimal start-date. For the purposes of illustration, let period t + j be the optimal start-date.

• The sequence of periods [t+j+1, t+k+3] serve as potential candidates for the end of the recession. The optimal end-date for the recession is chosen as follows:
  
  1. Periods with positive tension index values are eliminated.
  
  2. Beginning with the last period in the remaining group of potential end-dates, we eliminate periods with with contemporaneous growth rate greater than 2.75. The first period not eliminated is the optimal choice for the end of the recession.

Application of the above dating procedure to quarterly U.S. GDP data from 1950:III to 2008:I results in near accurate prediction of the starts and ends of recession. With the starts of recessions, the algorithm was off by one quarter on three occasions (1969:III, 1979:IV and 1981:IV were declared as starts for recessions whose NBER starts were 1969:IV, 1980:I and 1981:III respectively) and by two quarters on one occasion (the dating procedure prefers 2008:II to be the start of the recession deemed to have begun in 2007:IV by NBER). With the ends of recessions, the procedure was off on only one occasion: the recession with the NBER dated end in 1991:I was determined to be at 1991:III by our method.